Question: The length of a rectangle is four times its width. The perimeter is 100 cm. What is the number of square centimeters in the area of the rectangle?
Explanation: Let the length of the rectangle be $l$ and the width be $w$. We are trying to find the area of the rectangle, or $l \cdot w$, so we need to first find both $l$ and $w$. We can set up the following system of equations to represent the given information: \begin{align*} l &= 4w \\ 2l + 2w &= 100 \\ \end{align*} We will first solve for $w$ by eliminating $l$ from the equations above. Substituting the first equation into the second to eliminate $l$, we get $2(4w)+2w=100$ or $w=10$. Plugging this value into the first equation gives $l=4(10)=40$. Thus, the area of the rectangle is $l \cdot w = 40 \cdot 10 = \boxed{400}$ square centimeters.